The crash happened at 7.15pm on Sunday, April 7 on Holgate Road in York.
It involved the cyclist and a parked car.
The man, who is local to York and in his 50s, treated at the scene for serious head injuries.
He was taken by ambulance to Leeds General Infirmary, where he remains in a critical condition.
His next of kin have been informed.
-> Man arrested for attempted murder after Huddersfield shootingFollowing the collision, the road was closed for a number of hours to allow police to examine the scene.
North Yorkshire Police said the man was riding a yellow cycle, and wearing a grey sports top, blue cargo trousers and a khaki baseball cap.
They are now appealing for any witnesses or anyone with information to contact them on 101, quoting reference 12190062550